U.S. patent application number 11/988757 was filed with the patent office on 2009-12-03 for system and method for active detection of asymmetry in rotating structures.
Invention is credited to Izhak Bucher, Ofer Shomer.
Application Number | 20090293613 11/988757 |
Document ID | / |
Family ID | 37637590 |
Filed Date | 2009-12-03 |
United States Patent
Application |
20090293613 |
Kind Code |
A1 |
Bucher; Izhak ; et
al. |
December 3, 2009 |
System and Method for Active Detection of Asymmetry In Rotating
Structures
Abstract
System and method for active detection of asymmetry in a
rotating structure, the method comprises: imparting harmonic
mechanical excitation on the rotating structure that is
asynchronous to the speed of rotation of the structure; obtaining a
response from the excited rotating body; and analyzing the response
to determine a presence of modulation of the imparted harmonic
mechanical excitation, that causes vibration at a frequency that is
a combination of both the harmonic mechanical excitation and the
modulation speed of rotation.
Inventors: |
Bucher; Izhak; (Haifa,
IL) ; Shomer; Ofer; (Haifa, IL) |
Correspondence
Address: |
Pearl Cohen Zedek Latzer, LLP
1500 Broadway, 12th Floor
New York
NY
10036
US
|
Family ID: |
37637590 |
Appl. No.: |
11/988757 |
Filed: |
July 12, 2006 |
PCT Filed: |
July 12, 2006 |
PCT NO: |
PCT/IL2006/000811 |
371 Date: |
June 25, 2009 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
60698022 |
Jul 12, 2005 |
|
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|
Current U.S.
Class: |
73/462 |
Current CPC
Class: |
G01M 1/20 20130101; F03D
17/00 20160501 |
Class at
Publication: |
73/462 |
International
Class: |
G01M 1/16 20060101
G01M001/16 |
Claims
1. A system for active detection of asymmetry in a rotating
structure, the system comprising: at least one actuator for
introducing mechanical force that imparts harmonic mechanical
excitation on the rotating structure that is asynchronous to the
speed of rotation of the structure; at least one of a plurality of
sensors for sensing a response from the excited rotating body in
the form of vibrations of the rotating structure; a signal
processing unit for receiving the response and for analyzing the
response to determine a presence of modulation of the imparted
harmonic mechanical excitation, that causes vibration at a
frequency that is a combination of both the harmonic mechanical
excitation and the modulating speed of rotation.
2. The system as claimed in claim 1, wherein said at least one of a
plurality of sensors comprises one or more proximity sensors.
3. The system as claimed in claim 1, wherein said at least one
actuator comprises computer controlled active magnetic bearing.
4. The system as claimed in claim 1, wherein said at least one
actuator is incorporated in a motor that serves for rotating the
rotating structure.
5. A method for active detection of asymmetry in a rotating
structure, the method comprising: imparting harmonic mechanical
excitation on the rotating structure that is asynchronous to the
speed of rotation of the structure; obtaining a response from the
excited rotating body; and analyzing the response to determine a
presence of modulation of the imparted harmonic mechanical
excitation, that causes vibration at a frequency that is a
combination of both the harmonic mechanical excitation and the
modulating speed of rotation.
6. The method as claimed in claim 5, wherein the frequency of the
harmonic mechanical excitation is selected so that either
.omega.+2.OMEGA. or .omega.-2.OMEGA., or .omega.+n2.OMEGA., n being
a positive or negative integer, where .OMEGA. is the instantaneous
speed of rotation of the rotating structure and .omega. is the
frequency of the harmonic mechanical excitation, is about the
natural frequency of the rotating structure.
7. The method as claimed in claim 5, wherein the step of imparting
the harmonic mechanical excitation is achieved using at least one
actuator for introducing mechanical force on the rotating
structure.
8. The method as claimed in claim 7, wherein said at least one
actuator is incorporated in a motor that serves for rotating the
rotating structure.
9. The method as claimed in claim 7, wherein said actuator
comprises computer controlled active magnetic bearing.
10. The method as claimed in claim 5, wherein the step of obtaining
the response is achieved using at least one of a plurality of
sensors.
11. The method of claim 10, wherein said at least one of a
plurality of sensors comprises one or more proximity sensors.
12. The method as claimed in claim 5, wherein the step of analyzing
the response comprises using a signal processing unit for receiving
the response and for analyzing the response.
Description
FIELD OF THE INVENTION
[0001] The present invention relates to rotating structures. More
particularly the present invention relates to method and system for
detection of asymmetry in rotating structure.
BACKGROUND OF THE INVENTION
[0002] Mass and stiffness asymmetry in rotating machinery is often
the manifestation of developing imperfections or faults. Any
asymmetry in a rotating part adds a periodic term to the
coefficients of the equations of motion with a magnitude
proportional to the level of asymmetry and frequency of twice the
rotation speed. There are several factors affecting the response at
the speed of rotation and its multiples, therefore asymmetry has a
negligibly small effect on the response magnitude (vibration). At
these frequencies, asymmetry is very difficult to detect from the
naturally arising response at an early stage. In theory, many
faults do produce special features in the response in the form of
additional harmonics or modulation, but in practice, due to the
small magnitude of these signal components compared with the
unbalance and normal dynamic response, faults are only detected
when they are severe.
[0003] Asymmetry of a rotating system may arise from design
specifications, fulfilling certain engineering requirements (e.g.
wind turbines and impellers), or could be the result of developing
faults such as shaft crack, case rubbing or turbine blade failure.
In the latter, a dedicated diagnostic procedure of the rotating
structure is required to monitor the machine, as an aid to schedule
maintenance shut-downs, only when necessary. Mathematically,
asymmetric rotating systems are characterized by periodic (usually
harmonic) coefficients which may appear in the mass, damping or
stiffness matrices. These periodic terms, can cause a parametric
resonance or give rise to self excited vibrations.
[0004] Analytical and numerical tools for investigating time
varying systems include the Lyapunov-Floquet transformation whereby
a transition matrix transforms any Linear Time Periodic (LTP)
equation of motion to a linear time invariant (LTI) differential
equation.
[0005] In some rotating linear time variant systems, the
Floquet-Lyapunov transformation may take the form of a coordinate
system's transformation which results in constant coefficient
matrices. The transformation matrix is obtained by defining two
coordinate systems, inertial and rotating (body fixed).
[0006] Most of the publications related to rotordynamics focus on
critical speeds prediction balancing procedures and stability
analysis.
[0007] External excitation devices (e.g. magnetic bearings) open
new possibilities for active detection of faults. The main source
of excitation (misalignment and unbalance) in rotating machines
appears at the multiples of the speed of rotation. It is often the
case that a measurement of the normal response cannot be separated
from the effect of a developing fault since minute defects are
buried under larger signal components appearing at the same
frequencies. Active diagnostics, on the other hand, is capable of
injecting a dedicated interrogation force at non-synchronous
excitation frequencies and with the help of appropriate models of
the rotating system, a unique signal frequency that is the result
of a specific defect may be created. With this model-based
diagnostics, trending is no longer necessary and superior
detectability of certain faults can be achieved. The appearance of
tiny additional spectral lines in the presence of cracks was
observed by Bucher and Seibold ("A two-stage approach for enhanced
diagnosis of rotating machines", IFToM Conference on Rotor
Dynamics, Darmstadt, Germany, pp 338-349, September 1998), in which
both a model based and a signal based detection approach was
proposed.
[0008] The present invention seeks to exploit the advantages of
active diagnostics for the detection of asymmetry in the rotating
part, by utilizing an external excitation device (e.g. Active
Magnetic Bearing (AMB)) as a non-synchronous force exciter. The
steady state response, expressed in inertial coordinates is shown
to incorporate side-bands. While the carrier frequency is largely
related to the symmetric part of the system, the magnitude of
side-band frequency lines is associated with the level of asymmetry
in the system. The concept and implications of non-synchronous
excitation on the measured response are discussed hereinafter, with
reference to several models, for the more simplified of which,
analytical steady-state solutions are obtained. The rigid model is
used to reveal the inherent ability to actively detect asymmetry.
Flexible shaft models, in which the shaft's mass and gyroscopic
effects are neglected, are then derived and solved to prove the
advantages of the non-synchronous excitation over the synchronous
excitation scheme. Detecting rotating asymmetry in the presence of
anisotropic stator is demonstrated through an approximated solution
using Hill's infinite determinant.
[0009] We further investigate the gyroscopic effect on the
asymmetry detection. Using the Campbell diagram and the frequency
response at different rotation speeds, a working point (rotation
and excitation frequencies) is chosen, such that the modulated
response indicative to the asymmetry would resonate. Further, a
more realistic model in which finite element formulation is used
and the shaft's mass is taken into account. The detection of
asymmetry by means of non-synchronous excitation is demonstrated in
the presence of a combined synchronous and asynchronous excitation
sources.
BRIEF DESCRIPTION OF THE ON
[0010] There is thus provided, in accordance with some preferred
embodiments of the present invention, a system for active detection
of asymmetry in a rotating structure, the system comprising:
[0011] at least one actuator for introducing mechanical force that
imparts harmonic mechanical excitation on the rotating structure
that is asynchronous to the speed of rotation of the structure;
[0012] at least one of a plurality of sensors for sensing a
response from the excited rotating body in the form of vibrations
of the rotating structure; and
[0013] a signal processing unit for receiving the response and for
analyzing the response to determine a presence of modulation of the
imparted harmonic mechanical excitation, that causes vibration at a
frequency that is a combination of both the harmonic mechanical
excitation and the modulating speed of rotation.
[0014] Furthermore, in accordance with some preferred embodiments
of the present invention, said at least one of a plurality of
sensors comprises one or more proximity sensors.
[0015] Furthermore, in accordance with some preferred embodiments
of the present invention, said at least one actuator comprises
computer controlled active magnetic bearing.
[0016] Furthermore, in accordance with some preferred embodiments
of the present invention, said at least one actuator is
incorporated in a motor that serves for rotating the rotating
structure.
[0017] Furthermore, in accordance with some preferred embodiments
of the present invention, there is provided a method for active
detection of asymmetry in a rotating structure, the method
comprising:
[0018] imparting harmonic mechanical excitation on the rotating
structure that is asynchronous to the speed of rotation of the
structure;
[0019] obtaining a response from the excited rotating body; and
[0020] analyzing the response to determine a presence of modulation
of the imparted harmonic mechanical excitation, that causes
vibration at a frequency that is a combination of both the harmonic
mechanical excitation and the modulating speed of rotation.
[0021] Furthermore, in accordance with some preferred embodiments
of the present invention, the frequency of the harmonic mechanical
excitation is selected so that either .omega.+2.OMEGA. or
.omega.-2.OMEGA., or .omega.+n2.OMEGA., n being a positive or
negative integer, where .OMEGA. is the instantaneous speed of
rotation of the rotating structure and .omega. is the frequency of
the harmonic mechanical excitation, is about the natural frequency
of the rotating structure.
[0022] Furthermore, in accordance with some preferred embodiments
of the present invention, the step of imparting the harmonic
mechanical excitation is achieved using at least one actuator for
introducing mechanical force on the rotating structure.
[0023] Furthermore, in accordance with some preferred embodiments
of the present invention, said at least one actuator is
incorporated in a motor that serves for rotating the rotating
structure.
[0024] Furthermore, in accordance with some preferred embodiments
of the present invention, said actuator comprises computer
controlled active magnetic bearing.
[0025] Furthermore, in accordance with some preferred embodiments
of the present invention, the step of obtaining the response is
achieved using at least one of a plurality of sensors.
[0026] Furthermore, in accordance with some preferred embodiments
of the present invention, said at least one of a plurality of
sensors comprises one or more proximity sensors.
[0027] Furthermore, in accordance with some preferred embodiments
of the present invention, the step of analyzing the response
comprises using a signal processing unit for receiving the response
and for analyzing the response.
BRIEF DESCRIPTION OF THE FIGURES
[0028] In order to better understand the present invention, and
appreciate its practical applications, the following Figures are
provided and referenced hereafter. It should be noted that the
Figures are given as examples only and in no way limit the scope of
the invention. Like components are denoted by like reference
numerals.
[0029] FIG. 1 illustrates a rigid asymmetric rotor.
[0030] FIG. 2a illustrates a flexible massless shaft (deformed
shape) having inertia asymmetry.
[0031] FIG. 2b illustrates the coordinate system which was used in
the formulation (of the structure of FIG. 2a).
[0032] FIG. 3a illustrates a symmetric disc on an anisotropic shaft
(deformed shape).
[0033] FIG. 3b illustrates the coordinate system which was used in
the formulation (of the structure of FIG. 3a).
[0034] FIG. 4a illustrates an asymmetric rotor (deformed shape)
resting on elastic, anisotropic supports.
[0035] FIG. 4b illustrates the coordinate system which was used in
the formulation (of the structure of FIG. 4a).
[0036] FIG. 5 illustrates a flexible rotor rig experimental set up,
as was tested, according to the present invention.
[0037] FIG. 6 illustrates a block diagram of the experimental set
up, as was tested, according to the present invention.
[0038] FIG. 7 illustrates a plot of the response measured on the
experimental set-up with respect to frequency.
DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS
[0039] A main aspect of the present invention is the provision of a
method and system for detecting in-situ small asymmetry (or
asymmetries) in a rotating body. By "in-situ" is meant detection of
asymmetry during normal operation of the rotating body, without
having to stop its normal operation or without having to dismantle
it for separate examination. By "asymmetry is meant any
irregularity or imperfection in the distribution of mass and in the
distribution of stiffness in said body.
[0040] The present invention suggests introducing a harmonic
mechanical excitation that is asynchronous to the speed of rotation
of said body. The presence of asymmetry in the body brings about
modulation of the introduced harmonic mechanical excitation, that
causes vibration at a frequency that is a combination of both (the
harmonic excitation and the modulating speed of rotation).
.phi. . .apprxeq. Q e .OMEGA. J d .omega. cos .omega. t - Q e J d
.OMEGA. 2 .omega. .DELTA. J J m ( cos ( .omega. + 2 .OMEGA. ) t +
cos ( .omega. - 2 .OMEGA. ) t ) + O ( .DELTA. J 2 )
##EQU00001##
[0041] Where .phi. is the angular vibration response, .DELTA.J is
the deviation of the polar moment of inertia from its mean value,
whereas J.sub.m is the mean value of the polar moment of inertia
Q.sub.e is the amplitude of the asynchronous force, J.sub.d is
approximately J.sub.m and t is time. .OMEGA. is the instantaneous
speed of rotation, and .omega. is the frequency of the externally
introduced excitation.
[0042] The frequency of the externally introduced harmonic
excitation is selected such that the combined modulated frequency
yields maximal response levels, causing the small asymmetry to have
a maximal effect on the response at a distinct frequency.
[0043] The present invention does not seek to drive the entire
system at resonance frequencies as this may cause substantial
damage, but rather causes parametric excitation. In other words
large whirling amplitudes are not desired and hence avoided, while
at the same time small asynchronous oscillations of sufficient
magnitudes are generated.
[0044] Consider a rigid rotating shaft having a diagonal, constant,
tensor of inertia, I.sub.O in the e.sub.1'e.sub.2'e.sub.3' C.S:
I.sub.O=diag(J.sub.dJ.sub.pJ.sub.d)
[0045] which is free to precess on a frictionless plane around
e.sub.3', as shown in FIG. 1. The shaft is subject to a
non-synchronous torque around e.sub.3'.
[0046] Four identical point-masses (imperfections) m, are displaced
from the original centre of shaft (the origin o of the
e.sub.1'e.sub.2'e.sub.3' coordinate system (C.S.)), in a symmetric
distribution, creating two unequal diametrical moments of inertia
J.sub.x.noteq.J.sub.z, yet keeping the centre of mass unchanged so
the shaft remains statically and dynamically balanced. The reason
for examining a situation with four identical point masses arranged
symmetrically about the rotating shaft is meant to emphasize the
difference between this case and normal unbalanced situation. The
latter is quite common and is manifested by means of a vibration at
the frequency of rotation. This fact makes asymmetry difficult to
distinguish from normal unbalance situation.
[0047] The locations of the 4 masses are:
r.sub.1=.rho.e.sub.1'+le.sub.2', r.sub.2=-.rho.e.sub.1'+le.sub.2',
r.sub.3=.rho.e.sub.1'-le.sub.2',
r.sub.4=-.rho.e.sub.1'-le.sub.2'
[0048] Consequently, due to constant rotation speed
.OMEGA.e.sub.2', the tensor of inertia has time-periodic terms.
Newton's second law can be used to express the angular momentum of
the shaft in e.sub.1' e.sub.2'e.sub.3', as:
T G = t h G = h . G + .omega. ~ .times. h G ##EQU00002##
[0049] Where h.sub.G is the angular momentum around the centre of
mass (which coincide with the C.S. origin), and
.omega.=.phi.e.sub.3' is the angular velocity of
e.sub.1'e.sub.2'e.sub.3' with respect to an inertial frame. By
defining an external moment as
t Q ( t ) = Q _ e e 3 ' = - Q e sin ( .omega. t ) ,
##EQU00003##
and neglecting friction, the precession can be expressed as:
.phi. . = .OMEGA. / .omega.Q e cos ( .omega. t ) J x + J z 2 + J x
- J z 2 cos ( 2 .OMEGA. t ) ##EQU00004##
[0050] Where,
J m = J x + J z 2 = J d + 4 m l 2 + 2 m .rho. 2 , .DELTA. J = J x -
J z 2 = 2 m .rho. 2 . ##EQU00005##
Assuming that the mass imperfections are small, i.e. J.sub.d=4
ml.sup.2+2 m.rho..sup.2, and defining the asymmetry ratio (ASR)
.DELTA. J J m .apprxeq. 2 m .rho. 2 J d , ##EQU00006##
the last equation simplifies into:
.phi. . = .OMEGA. J d .omega. Q e cos ( .omega. t ) 1 + .DELTA. J J
m cos ( 2 .OMEGA. t ) ##EQU00007##
[0051] Since the asymmetry is small, the last equation may be
expanded in a Taylor series:
.phi. . .apprxeq. Q e .OMEGA. J d .omega. cos .omega. t - Q e J d
.OMEGA. 2 .omega. .DELTA. J J m ( cos ( .omega. + 2 .OMEGA. ) t +
cos ( .omega. - 2 .OMEGA. ) t ) + O ( .DELTA. J 2 )
##EQU00008##
[0052] It can be noticed that the asymmetry is manifested by the
addition of two modulated frequency components at
.omega..+-.2.OMEGA. in the response, having amplitude proportional
to the imperfection .DELTA.J. Indeed these terms become more
significant at lower excitation frequencies, but the ASR is
expected to be rather small and therefore the asymmetry may be
difficult to detect without special means. It is clear from the
last equation that the combination of rotation and an asynchronous
external excitation isolates the asymmetry related term which can
thus serve as a unique indicator for the level of non-uniformity in
the angular mass distribution.
[0053] One of the measures one can take to amplify the asymmetry
related signal components is to tune the excitation frequency until
these terms become detectable. For this purpose a flexible shaft
system must be investigated, and the natural amplification of
elastic structures can be exploited.
[0054] When rotating asymmetry is present, two main cases can be
considered: (i) Asymmetric mass distribution, namely different
diametrical moments of inertia. (ii) Anisotropic shaft
stiffness.
[0055] Consider a rigid disc with asymmetric diametrical moments of
inertia (FIG. 2b) mounted on a massless, flexible shaft as depicted
in FIG. 2a. The mathematical representation of the response of the
system depicted in this figure to an external rotating excitation
of magnitude Q.sub.e and frequency .omega. is given by:
( .theta. x .theta. z ) .apprxeq. - Q e J m ( .omega. 2 - .omega. n
2 ) ( cos .omega. t sin .omega. t ) + .omega. ( 2 .OMEGA. - .omega.
) Q e 4 J m ( .omega. 2 - .omega. n 2 ) ( .OMEGA. - .omega. +
.omega. n 2 ) ( .OMEGA. - .omega. - .omega. n 2 ) ( .DELTA. J J m )
( cos ( .omega. - 2 .OMEGA. ) t sin ( .omega. - 2 .OMEGA. ) t )
with .DELTA. J = J z - J z 2 , J m = J z + J x 2 , .omega. n 2 = k
~ J m ( 1 ) ##EQU00009##
[0056] While only one frequency appears in rotating coordinate
system (C.S.), the inertial C.S. steady state response is
characterized by two frequencies. The coefficient of the modulated
frequency .omega.-2.OMEGA. is proportional to the asymmetry ratio
(ASR) which is
.DELTA. J J m , ##EQU00010##
while the response at the frequency of excitation .omega. is
independent of the system's asymmetry. With no asymmetry, i.e. when
.DELTA.J.ident.0, only the first term remains.
[0057] The value of last function becomes very large when the
asynchronous excitation frequency is either
.omega.=.+-..omega..sub.n or .omega.=2.OMEGA..+-..omega..sub.n. In
the latter case, the large response is attributed to a parametric
excitation that appears only when the system contains the asymmetry
related, time-varying coefficients. Other notable values are
received for .omega.+n2.OMEGA., n being a positive or negative
integer.
[0058] A more suitable selection of the external excitation
frequency would make the response at the modulated frequency
.omega.-2.OMEGA. a sensitive function of the ASR. An externally,
asynchronous excitation can thus be tuned to detect small levels of
mass asymmetry if .omega.-2.OMEGA. is chosen close to one of the,
speed-dependent, natural frequencies -.omega..sub.n.
[0059] Following the discussion above, the question arises, whether
anisotropic rotating stiffness, that approximates mathematically
transverse cracks in the shaft, could be detected by the same
approach, i.e. by means of non-synchronous excitation. FIG. 3a
depicts a perfectly balanced, symmetric disc mounted on a massless,
yet flexible, anisotropic shaft (the coordinate system is shown in
FIG. 3b). As in the previous model, the e.sub.1'e.sub.2'e.sub.3',
C.S. rotates with the shaft at a constant speed .OMEGA. around the
e.sub.2' axis and the disc is free to precess in two orthogonal
planes (e.sub.1'e.sub.2' and e.sub.3'e.sub.2'). In the case of an
asymmetric shaft the mathematical representation of the angular
response to the externally introduced excitation is given by:
( .theta. x .theta. z ) .apprxeq. Q e .omega. n 2 k ~ m ( .omega. n
2 - .omega. 2 ) ( cos .omega. t sin .omega. t ) + Q e .omega. n 4
.DELTA. k ~ k ~ m 4 k ~ m ( .omega. 2 - .omega. n 2 ) ( .OMEGA. -
.omega. + .omega. n 2 ) ( .OMEGA. - .omega. - .omega. n 2 ) ( cos (
.omega. - 2 .OMEGA. ) t sin ( .omega. - 2 .OMEGA. ) t ) ( 2 )
##EQU00011##
where k ~ m = k ~ z + k ~ x 2 and .DELTA. k ~ = k ~ z - k ~ x 2
##EQU00012##
are the mean and deviatory stiffness respectively, and
.omega. n 2 = k ~ m J d ##EQU00013##
is the averaged, squared natural frequency.
[0060] The anisotropy creates a unique frequency component at
.omega.-2.OMEGA. in the presence of asynchronous excitation. Since
the modulated, non-synchronous response is directly proportional to
the stiffness anisotropy, it can serve as a good indicator for this
type of faults when a suitable excitation frequency is chosen.
[0061] It is often the case that the rotating asymmetric element
rests on foundations with anisotropic stiffness. The model of
asymmetric rotating mass mounted on anisotropic stator stiffness
(FIG. 4a, the coordinate system illustrated in FIG. 4b), is
characterized by periodic coefficients in the EoM (Equation of
Motion), both in inertial and rotating C.S. Finding the
transformation that would render the EoM time invariant is somewhat
more difficult than what was shown above and the use of the Floquet
Lyapunov Theory (FLT) and transformation is necessary. An
alternative way to solve the LTV equations having periodically
varying coefficients, the so called Hill's Infinite Determinant
method (HID) is employed. In this approach, a suitable, closed
form, approximation in a multi-frequency form is derived.
[0062] The response of a general rotating system resting on a
general type of foundation is given by:
q(t).apprxeq.q.sub.0e.sup.J.omega.t+
q.sub.0e.sup.-J.omega.t+q.sub.1e.sup.J(.omega.+2.OMEGA.)t+
q.sub.1e.sup.-J(.omega.+2.OMEGA.)t+q.sub.-1e.sup.J(.omega.-2.OMEGA.)t+
q.sub.-1e.sup.-J(.omega.-2.OMEGA.)t
[0063] Where q(t) is a vector of N degrees of freedom.
The solution of this equation is expanded in a multi-variable
Taylor series in both .DELTA. k. If the anisotropy can be
considered small, then the series is truncated at O(.DELTA.
k.sup.2) and O(.DELTA.J.sup.2), resulting in:
q - 1 .apprxeq. .omega. ( 2 .OMEGA. - .omega. ) Q e 8 J m ( .omega.
2 - .omega. n 2 ) ( .OMEGA. - .omega. + .omega. n 2 ) ( .OMEGA. -
.omega. - .omega. n 2 ) ( .DELTA. J J m ) ( j 1 ) ##EQU00014##
[0064] Clearly, the expression for q.sub.-1 provides exactly the
same result as in the case with asymmetric disc mounted on massless
shaft (FIG. 1a). This equation demonstrates that the foundation
asymmetry does not affect the ability to detect the asymmetry in
the rotating part.
[0065] External excitation devices (e.g. Active Magnetic Bearing
(AMB)) open new possibilities for active detection of faults.
[0066] In order to verify the proposed algorithm for detection of
asymmetric rotors, according to the present invention, two test
rigs were constructed: rigid rotor mounted on a soft table
balancing machine, and flexible rotor rig (we refer to the latter
experiment hereinafter).
[0067] The terms rigid and flexible are thought of in terms of
geometry and speed of rotation of the system.
[0068] Two types of non-synchronous excitation devices were used.
For the rigid rotor, a piezo-electric proof mass actuator, capable
of applying non-rotating, harmonic excitations, was mounted on the
balancing table. The flexible rotor experiment utilized an active
magnetic bearing, able to exert spatially rotating forces at
various frequencies.
[0069] The flexibility of a rotating system is considered with
respect to its geometrical dimensions as well as the speed of
rotation. The flexible-shaft based experimental system is depicted
in FIG. 5, illustrating a flexible rotor rig set-up. A indicates a
flexible disk containing small asymmetry, B indicates ball-bearing
stand, C indicates sensors holder (for response measurements), D
indicates Cut-out of the active magnetic bearing external force, E
indicates bearing stand, and F indicates the electric motor.
[0070] In this experiment the shaft was 1 [m] long, its diameter 20
[mm], with one disc of diameter 300 [mm], and 3 [mm] thickness,
mounted at its free end. Masses can be added to the disc to create
an asymmetric inertia distribution. The shaft was connected to a
servo motor through a bellows type constant velocity joint, and was
supported by two self-aligning ball bearings. One, computer
controlled, Active Magnetic Bearing (AMB) was located along the
shaft and served as a non-synchronous exciter. In order to balance
the system, two, Aluminum balancing planes of diameter 150 [mm]
were added along the shaft. Being flexible, deformations of the
shaft can be sensed directly; hence several proximity sensors were
placed along the shaft both in horizontal and vertical position.
The experimental system represents a realistic rotating structure
where both the shaft and the supports are not perfect, and the
rotation introduces gyroscopic effect. The actuator for imparting
the asynchronous excitation on the rotating body can be
incorporated and integrated with the motor that rotates the body.
The measurements indicated hereinabove were the measurements used
in the experiment and in no way limit the scope of the present
invention.
[0071] It was shown that the steady-state response due to a
non-synchronous force in two perpendicular planes contains 2
frequencies of vibrations. While vibrations at the frequency of
excitation .omega. are related to the mean moment of inertia (the
symmetric part) of the system, the vibration at the modulated
frequency 2.OMEGA.-.omega. is exclusively associated with the
deviatory moment of inertia of the system .DELTA.J. While the
former frequency appears in the total response regardless of the
ASR, the latter materializes only when .DELTA.J.noteq.0, thus
serves as an indicator of the asymmetry in the system.
[0072] In a parametric study, the frequency of excitation--.omega.
was varied for every shaft speed--.OMEGA.. Thus, for a given system
with well known physical properties (moments of inertia, bending
stiffness etc.) and a non-synchronous force of known amplitude,
with predefined locations for the force excitation and measured
response, the optimal sensitivity of the asymmetry related term in
the response, (in the .OMEGA.-.omega. plane) was obtained.
[0073] Eddy current proximity sensors were used. Since measurements
are of the deformed shaft, XL 3300 proximity sensors from
Bently-Navada.TM. were employed.
[0074] Analogue signals from the sensors are measured by the
HP-Agilent.TM. VXI measurement system. An additional, analogue,
resolver-to-encoder signal is produce by the motor controller and
used as a reference phase signal.
[0075] The dSPACE.TM. system is used to communicate with the motor
controller and control the AMB.
[0076] A schematic view of the experiment setup is depicted in FIG.
6.
[0077] The non-synchronous frequency at which the AMB should excite
the system should be chosen such that the modulated, indicative
frequency component (.omega..+-.2.OMEGA.) would coincide with a
natural frequency.
.omega.=2.pi.f.sub.max+2.OMEGA.=2.pi.101.5 [Rad/sec]
[0078] Two rotor types were examined: symmetric and asymmetric. The
system was tested under three different modes of operation to
assess its effect on the measured response:
[0079] No control--Active Magnetic bearing (AMB) is off.
[0080] With control--AMB is operating in closed-loop attempting to
maintain zero displacement in both axes.
[0081] With Non-synchronous excitation--AMB is operating in close
loop, trying to maintain a sinusoidal motion (for each axis) at
101.5 [Hz] (90.degree. phase lag between the axes, guarantying
constant amplitude, spatially rotating force is generated).
[0082] For each configuration (of rotor and control), four types of
experiments were performed:
[0083] (i). Steady state response--at .OMEGA.=2175 [RPM]. With 1%
asymmetry, with and without closed-loop control
[0084] (ii) Steady state response--at .OMEGA.=2175 [RPM]. Without
asymmetry with and without closed-loop control
[0085] Measurements were taken at a sampling frequency of
f.sub.s=2560 [Hz].
[0086] Upon reaching steady state, measurements were sampled and
amplitude estimation was carried out (by means of least squares),
which considered the responses at the speed of excitation to, speed
of rotation .OMEGA., positive and negative modulated frequencies
.omega..+-.2.OMEGA. and the first seven harmonics of the frequency
of rotation n.OMEGA., n=2/8. The results of the amplitude
estimation for the fundamental speeds appear in Table 1.
TABLE-US-00001 Experiment Amplitude estimation (in .mu.m) at speed
Rotor type type .OMEGA. .omega. .omega. - 2.OMEGA. .omega. +
2.OMEGA. Symmetric w\o control N\A N\A N\A N\A rotor w\control 121
0.01 0.072 0.006 w\excitation 12.7 8.67 0.284 0.81 Asymmetric w\o
control 26.25 0.011 0.002 0.004 rotor w\control 20.35 0.006 0.053
0.013 w\excitation 137 8.96 14.16 13.3
[0087] Table 1 reveals that the modulated signals are two orders of
magnitude higher in the asymmetric rotor in comparison to the
symmetric rotor thus serving as a good indicator to the asymmetry.
While differences are also visible in the amplitudes at the speed
of rotation .OMEGA. between the two cases, they are related to the
effectiveness of the balancing procedure performed on each rotor
and not directly to the amount of asymmetry. In addition, the
amplitudes of the asymmetric rotor at the speed of rotation and
speed of excitation are higher in the case of no control than in
the case of zero reference control, which demonstrates the added
value of the AMB as a damping element in the system. Analysis of
the steady state response in the frequency domain was carried out
by means of FFT. The differences in the spectrum of vibration in
the presence of non-synchronous excitation are visible in FIG. 7,
where the modulated frequencies .omega..+-.2.OMEGA. exhibit the
biggest change in magnitude between the symmetric and asymmetric
configurations, regardless of the level of unbalance in the system.
Indeed, the fundamental speed of rotation and its harmonics also
change between the configurations but this change may be related to
the effectiveness of the balancing procedure. Moreover, in real
applications, the change in these frequencies may not be
exclusively associated with asymmetry change as other, unpredicted,
phenomena may affect the same spectral lines.
[0088] The suggested detection scheme is applicable for rigid and
flexible rotors. An AMB was incorporated into a flexible rotor test
rig and applied non-synchronous excitation forces. A frequency
response carried out on the rotating rig helped determine the
optimal excitation frequency such that the expected sidebands would
be excited in or near resonance.
[0089] It should be clear that the description of the embodiments
and attached Figures set forth in this specification serves only
for a better understanding of the invention, without limiting its
scope.
[0090] It should also be clear that a person skilled in the art,
after reading the present specification could make adjustments or
amendments to the attached Figures and above described embodiments
that would still be covered by the present invention.
* * * * *